A public key and digital signature is provided using a private key of a public-private key pair in an elliptic curve digital signature algorithm (ECDSA) by: identifying domain parameters of an elliptic curve for use in elliptic curve cryptography, the domain parameters including an initial generating point; transforming the generating point into a new generating point as a deterministic function; generating the public key as a deterministic function of the private key and the domain parameters, in which the new generating point is substituted for the initial generating point; and generating the digital signature as a function of the private key and the domain parameters, in which the new generating point is substituted for the initial generating point.